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Towards better data structures: From atoms via compound terms to - - PowerPoint PPT Presentation

Dec 04, 2023 115 likes •301 views

Towards better data structures: From atoms via compound terms to feature-structures Detmar Meurers: Intro to Computational Linguistics I OSU, LING 684.01, 26. February 2003 Overview From atoms to typed-feature structures What do

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Towards “better” data structures: From atoms via compound terms to feature-structures

Detmar Meurers: Intro to Computational Linguistics I OSU, LING 684.01, 26. February 2003

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Overview

  • From atoms to typed-feature structures
  • What do non-atomic data structures represent?
  • Combining non-atomic data structures
  • Term unification
  • Representing feature structures
  • Feature structure unification

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From atoms to typed-feature structures

  • atoms, e.g. verb_trans_first_sing_fin
  • compound terms, e.g.

verb(first,sing,fin,[noun(first,sing,nom,[]),noun(_,_,acc,[])])

  • feature structures, e.g.

category: verb, vform: fin, person: first, number: sing, subcat: [(category: noun, case:noun, person:first, number:sing, subcat: []), (category: noun, case:acc, subcat: [])]

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  • typed feature structures, e.g.

category: (verb, vform: (fin, agr:(person: first, number: sing)), subcat: [(category: (noun, case:nom, agr: (person:first, number:sing), subcat: [])), (category: (noun, case:acc, subcat: []))])

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What do non-atomic data structures represent?

s --> np(Per,Num), vp(Per,Num). The rule represents a set of ground instances, one for each possible substitution of a variable with a value. s --> np(first,sing), vp(first,sing). s --> np(second,sing), vp(second,sing). s --> np(third,sing), vp(third,sing). s --> np(first,plur), vp(first,plur). s --> np(second,plur), vp(second,plur). s --> np(third,plur), vp(third,plur).

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Combining compound terms

np(third,sing) --> [he]. np(third,plur) --> [they]. vp(third,sing) --> [walks]. vp(third,plur) --> [walk]. s --> np(Per,Num), vp(Per,Num). Two possible substitutions:

  • Per=third and Num=sing
  • Per=third and Num=plur

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Most general unifiers

termUnify(f(X,h(Y, e),g(d(Z),e)), f(Y,h(d(Z),e),g(Y, e))). Which substitution should one report?

  • X=d(a)
  • X=d(b)
  • X=d(h(a,b))
  • . . .

Compute the most general unifier (MGU):

  • X=d(Z)

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Infinite trees

  • What happens when one unifies

– f(X) with X ? – f(a,g(X,b)) with X ?

  • Add an occurs check to test whether the variable occurs in the term.
  • In practice too costly.

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Term unification

  • A variable unifies with any term it does not occur in.
  • An atom unifies only with an identical atom.
  • Compound terms unify

– if their functors are identical and – their arguments unify pairwise, and the substitutions obtained as a result of each of these unifications are compatible.

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Converting predicates to lists (and vice versa) in Prolog

Prolog has a built-in predicate =.. to relate predicates to lists, i.e. Predicate =.. [Functor,Arg1,...,ArgN]. For example: functor(a(b),c,d) =.. [functor,a(b),c,d]. This also works for zero-arity functors, i.e. constants: a =.. [a].

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Explicit term unification in Prolog

termUnify(X,Y) :- (var(X) ;var(Y)), !, X = Y. termUnify(X,Y) :- X =.. [XFunctor|XArgs], Y =.. [YFunctor|YArgs], XFunctor=YFunctor, % test for atom identity unifyArgs(XArgs,YArgs). unifyArgs([],[]). unifyArgs([X|Xs],[Y|Ys]) :- termUnify(X,Y), unifyArgs(Xs,Ys).

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Representing feature structures in Prolog

  • The operator “:” is defined to separate feature:value

?- op(500,xfy,:).

  • Feature names and atomic values represented by Prolog atoms
  • Prolog variables encode structure sharing.
  • Feature structures represented as Prolog lists with open tails:

– [person:third, num:sing|_] – [person:X, num:sing, head:subj:person:X|_]

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Unifying feature structures in Prolog

unify(Dag,Dag) :- !. unify([Feat:Val | Rest1], Dag) :- pathval(Dag,Feat,Val,Rest2), unify(Rest1,Rest2) pathval([Feat:Val1 | Rest], Feat, Val2, Rest) :- !, unify(Val1,Val2). pathval([Dag | Rest], Feat, Val, [Dag | Rest2]) :- pathval(Rest,Feat,Val,Rest2).

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Towards grammar rules in PATR

rule(S,[NP,VP]) :- pathval(S,cat,s,_), pathval(NP,cat,np,_), pathval(VP,cat,vp,_), pathval(NP,per,X,_), pathval(VP,per,X,_), pathval(NP,num,Y,_), pathval(VP,num,Y,_).

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Grammar rules in PATR

?- op(500,xfy,:). ?- op(500,xfx,--->). ?- op(600,xfy,===). S ---> [NP,VP] :- S:cat === s, NP:cat === np, VP:cat === vp, NP:per === X, VP:per === X, NP:num === Y, VP:num === Y.

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Assigning a general meaning to “===”

X === Y :- denotes(X,Z), denotes(Y,Z). denotes(Var,Var) :- var(Var),!. denotes(Atom,Atom) :- atomic(Atom),!. denotes(Dag:Feat,Value) :- pathval(Dag,Feat,Value,_). pathval([Feat:Val1 | Rest], Feat, Val2, Rest) :- !, unify(Val1,Val2).

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pathval([Dag | Rest], Feat, Val, [Dag | Rest2]) :- pathval(Rest,Feat,Val,Rest2).

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